Question

Check whether the pair of linear equations 4x - 5y = 8 and 6x + 7y = 9 are consistent
or inconsistent. If consistent then obtain the solution graphically.​

Answer 1

Let a

1

x+b

1

y+c

1

=3x+2y−5 and a

2

x+b

2

y+c

2

=2x−3y−7

So, here a

1

=3; b

1

=2; c

1

=−5; a

2

=2; b

2

=−3; c

2

=−7

⇒

a

2

a

1

=

2

3

⇒

b

2

b

1

=

3

−2

⇒

a

2

a

1



=

b

2

b

1

Hence the system of equations has unique solution.

Thus the pair of equations are consistent